Subgroups — C₁₉×#20598 #18026557

Order 4864.

5982 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#418	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1786	C₂	1	8	yes	maximal, complemented
6	C₂⁶×C₁₉	—	2	1	no	—
7	C₂³×D₄×C₁₉	—	2	16	no	—
8	C₂³×D₄×C₁₉	—	2	2	no	—
9	C₂³×D₄×C₁₉	—	2	1	no	—
10	C₂³×D₄×C₁₉	—	2	4	no	—
11	C₂³×D₄×C₁₉	C₄	1	8	yes	complemented
12	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
13	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
16	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
17	C₁₉×#418	—	2	16	no	—
18	C₂×C₁₉×#102	C₂²	1	16	yes	complemented
19	C₁₉×#407	—	2	4	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
21	C₁₉×#381	—	2	1	no	—
22	C₁₉×#380	C₂²	1	4	yes	complemented
23	C₁₉×#379	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
25	C₂⁵×C₁₉	—	2	16	no	—
26	C₂⁵×C₁₉	—	2	8	no	—
27	C₂⁵×C₁₉	—	2	4	no	—
28	C₂⁵×C₁₉	—	2	2	no	—
29	C₂⁵×C₁₉	—	4	16	no	—
30	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₉	—	2	16	no	—
32	C₂²×D₄×C₁₉	—	2	32	no	—
33	C₂²×D₄×C₁₉	—	2	64	no	—
34	C₂²×D₄×C₁₉	—	2	64	no	—
35	C₂²×D₄×C₁₉	—	2	32	no	—
36	C₂²×D₄×C₁₉	—	2	8	no	—
37	C₂²×D₄×C₁₉	—	2	16	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	8	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	8	no	—
42	C₂²×D₄×C₁₉	—	2	4	no	—
43	C₂²×D₄×C₁₉	C₂×C₄	1	16	yes	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
45	C₂²×D₄×C₁₉	D₄	1	16	yes	—
46	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₉	—	2	8	no	—
48	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₁₉	D₄	1	2	yes	—
50	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	D₄	1	4	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₁₉	—	2	4	no	—
55	C₂×M₁₆×C₁₉	—	2	8	no	—
56	C₂²×C₈×C₁₉	C₂³	1	4	yes	complemented
57	C₁₉×#117	—	2	8	no	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	complemented
59	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄²×C₁₉	—	2	2	no	—
62	C₁₉×#102	—	2	32	no	—
63	C₁₉×C₂²⋊C₈	—	2	8	no	—
64	C₁₉×#95	—	2	4	no	—
65	C₂⁴×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	8	no	—
67	C₂⁴×C₁₉	—	2	32	no	—
68	C₂⁴×C₁₉	—	2	64	no	—
69	C₂⁴×C₁₉	—	2	16	no	—
70	C₂⁴×C₁₉	—	2	8	no	—
71	C₂⁴×C₁₉	—	2	16	no	—
72	C₂⁴×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	—	4	128	no	—
74	C₂⁴×C₁₉	—	4	16	no	—
75	C₂⁴×C₁₉	—	4	16	no	—
76	C₂⁴×C₁₉	—	4	64	no	—
77	C₂⁴×C₁₉	—	4	16	no	—
78	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
81	C₂×D₄×C₁₉	—	2	32	no	—
82	C₂×D₄×C₁₉	—	2	64	no	—
83	C₂×D₄×C₁₉	—	2	64	no	—
84	C₂×D₄×C₁₉	—	2	128	no	—
85	C₂×D₄×C₁₉	—	2	64	no	—
86	C₂×D₄×C₁₉	—	2	16	no	—
87	C₂×D₄×C₁₉	—	2	16	no	—
88	C₂×D₄×C₁₉	—	2	8	no	—
89	C₂×D₄×C₁₉	—	2	32	no	—
90	C₂×D₄×C₁₉	—	2	16	no	—
91	C₂×D₄×C₁₉	—	2	8	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	C₂²⋊C₄	1	32	yes	complemented
94	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
95	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	16	no	—
98	C₂²×C₄×C₁₉	—	2	8	no	—
99	C₂²×C₄×C₁₉	—	2	16	no	—
100	C₂²×C₄×C₁₉	—	2	8	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₁₉	—	4	8	no	—
113	C₂×C₈×C₁₉	—	2	4	no	—
114	C₂×C₈×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	8	no	—
116	C₂²⋊C₄×C₁₉	—	4	4	no	—
117	C₂²⋊C₄×C₁₉	—	4	8	no	—
118	C₄²×C₁₉	—	4	4	no	—
119	#20598	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	32	no	—
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	2	4	no	—
123	C₂³×C₁₉	—	2	4	no	—
124	C₂³×C₁₉	—	2	8	no	—
125	C₂³×C₁₉	—	2	16	no	—
126	C₂³×C₁₉	—	2	64	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	2	16	no	—
129	C₂³×C₁₉	—	2	32	no	—
130	C₂³×C₁₉	—	4	256	no	—
131	C₂³×C₁₉	—	4	32	no	—
132	C₂³×C₁₉	—	4	32	no	—
133	C₂³×C₁₉	—	4	64	no	—
134	C₂³×C₁₉	—	4	128	no	—
135	C₂³×C₁₉	—	4	16	no	—
136	C₂³×C₁₉	—	4	32	no	—
137	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
139	C₂³×C₁₉	#120	1	4	yes	—
140	C₂³×C₁₉	AGL(1,ℤ/8)	1	8	yes	—
141	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₁₉	—	2	64	no	—
143	D₄×C₁₉	—	2	8	no	—
144	D₄×C₁₉	—	2	16	no	—
145	D₄×C₁₉	—	2	32	no	—
146	D₄×C₁₉	C₂×C₂²⋊C₄	1	16	yes	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	8	no	—
150	C₂×C₄×C₁₉	—	2	8	no	—
151	C₂×C₄×C₁₉	—	2	16	no	—
152	C₂×C₄×C₁₉	—	4	4	no	—
153	C₂×C₄×C₁₉	—	4	8	no	—
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
156	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₉	#120	1	8	yes	—
158	C₂×C₄×C₁₉	#120	1	4	yes	—
159	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₁₉	—	4	4	no	—
163	C₂⁴×D₄	C₂×C₁₉	1	1	yes	characteristic
164	C₂×#418	C₂×C₁₉	1	4	yes	complemented
165	C₂×#407	C₂×C₁₉	1	1	yes	characteristic, complemented
166	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
167	#1786	C₂×C₁₉	1	8	yes	complemented
168	C₂²×C₁₉	—	2	32	no	—
169	C₂²×C₁₉	—	2	4	no	—
170	C₂²×C₁₉	—	2	4	no	—
171	C₂²×C₁₉	—	2	8	no	—
172	C₂²×C₁₉	—	2	16	no	—
173	C₂²×C₁₉	—	2	4	no	—
174	C₂²×C₁₉	—	2	16	no	—
175	C₂²×C₁₉	—	4	64	no	—
176	C₂²×C₁₉	—	4	128	no	—
177	C₂²×C₁₉	—	4	16	no	—
178	C₂²×C₁₉	—	4	32	no	—
179	C₂²×C₁₉	#379	1	4	yes	—
180	C₂²×C₁₉	#418	1	8	yes	complemented
181	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×#120	1	2	yes	—
183	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
184	C₄×C₁₉	—	2	4	no	—
185	C₄×C₁₉	—	8	4	no	—
186	C₄×C₁₉	#379	1	4	yes	—
187	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
188	C₄×C₁₉	C₂×#120	1	2	yes	—
189	C₂⁶	—	2	1	no	—
190	C₂³×D₄	—	2	16	no	—
191	C₂³×D₄	—	2	2	no	—
192	C₂³×D₄	—	2	1	no	—
193	C₂³×D₄	—	2	4	no	—
194	C₂³×D₄	C₄×C₁₉	1	8	yes	complemented
195	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
196	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
197	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
198	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
199	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
200	#418	—	2	16	no	—
201	C₂×#102	C₂²×C₁₉	1	16	yes	complemented
202	#407	—	2	4	no	—
203	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	complemented
204	#381	—	2	1	no	—
205	#380	C₂²×C₁₉	1	4	yes	complemented
206	#379	—	2	1	no	—
207	C₄×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₁₉	—	2	4	no	—
209	C₂×C₁₉	—	2	8	no	—
210	C₂×C₁₉	—	4	16	no	—
211	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
212	C₂×C₁₉	C₂×#418	1	2	yes	—
213	C₂×C₁₉	#3003	1	4	yes	—
214	C₂⁵	—	2	16	no	—
215	C₂⁵	—	2	8	no	—
216	C₂⁵	—	2	4	no	—
217	C₂⁵	—	2	2	no	—
218	C₂⁵	—	4	16	no	—
219	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
220	C₂²×D₄	—	2	16	no	—
221	C₂²×D₄	—	2	64	no	—
222	C₂²×D₄	—	2	32	no	—
223	C₂²×D₄	—	2	64	no	—
224	C₂²×D₄	—	2	32	no	—
225	C₂²×D₄	—	2	8	no	—
226	C₂²×D₄	—	2	16	no	—
227	C₂²×D₄	—	2	4	no	—
228	C₂²×D₄	—	2	8	no	—
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	—	2	8	no	—
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	C₂×C₄×C₁₉	1	16	yes	—
233	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
234	C₂²×D₄	D₄×C₁₉	1	16	yes	—
235	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
236	C₂³×C₄	—	2	8	no	—
237	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
238	C₂³×C₄	D₄×C₁₉	1	2	yes	—
239	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	D₄×C₁₉	1	4	yes	—
241	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂×M₁₆	—	2	4	no	—
244	C₂×M₁₆	—	2	8	no	—
245	C₂²×C₈	C₂³×C₁₉	1	4	yes	complemented
246	#117	—	2	8	no	—
247	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	complemented
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₄²	—	2	2	no	—
251	#102	—	2	32	no	—
252	C₂²⋊C₈	—	2	8	no	—
253	#95	—	2	4	no	—
254	C₁₉	#20598	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	2	64	no	—
258	C₂⁴	—	2	32	no	—
259	C₂⁴	—	2	16	no	—
260	C₂⁴	—	2	8	no	—
261	C₂⁴	—	2	16	no	—
262	C₂⁴	—	2	4	no	—
263	C₂⁴	—	4	128	no	—
264	C₂⁴	—	4	64	no	—
265	C₂⁴	—	4	16	no	—
266	C₂⁴	—	4	16	no	—
267	C₂⁴	—	4	16	no	—
268	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
269	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
270	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
271	C₂×D₄	—	2	64	no	—
272	C₂×D₄	—	2	32	no	—
273	C₂×D₄	—	2	128	no	—
274	C₂×D₄	—	2	64	no	—
275	C₂×D₄	—	2	64	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	16	no	—
279	C₂×D₄	—	2	16	no	—
280	C₂×D₄	—	2	32	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	C₂²⋊C₄×C₁₉	1	32	yes	complemented
284	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
285	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	16	no	—
288	C₂²×C₄	—	2	16	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
298	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
300	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
302	M₁₆	—	4	8	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	8	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	8	no	—
308	C₄²	—	4	4	no	—
309	C₂³	—	2	32	no	—
310	C₂³	—	2	8	no	—
311	C₂³	—	2	16	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	64	no	—
316	C₂³	—	2	32	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	2	16	no	—
319	C₂³	—	4	256	no	—
320	C₂³	—	4	64	no	—
321	C₂³	—	4	128	no	—
322	C₂³	—	4	32	no	—
323	C₂³	—	4	32	no	—
324	C₂³	—	4	32	no	—
325	C₂³	—	4	16	no	—
326	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
327	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
328	C₂³	C₁₉×#120	1	4	yes	—
329	C₂³	C₁₉×AGL(1,ℤ/8)	1	8	yes	—
330	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
331	D₄	—	2	64	no	—
332	D₄	—	2	32	no	—
333	D₄	—	2	8	no	—
334	D₄	—	2	16	no	—
335	D₄	C₂×C₂²⋊C₄×C₁₉	1	16	yes	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	16	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
346	C₂×C₄	C₁₉×#120	1	4	yes	—
347	C₂×C₄	C₁₉×#120	1	8	yes	—
348	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
350	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
351	C₈	—	4	4	no	—
352	C₂²	—	2	32	no	—
353	C₂²	—	2	8	no	—
354	C₂²	—	2	16	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	16	no	—
359	C₂²	—	4	64	no	—
360	C₂²	—	4	128	no	—
361	C₂²	—	4	32	no	—
362	C₂²	—	4	16	no	—
363	C₂²	C₁₉×#379	1	4	yes	—
364	C₂²	C₁₉×#418	1	8	yes	complemented
365	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
366	C₂²	C₂×C₁₉×#120	1	2	yes	—
367	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	4	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	8	4	no	—
370	C₄	C₁₉×#379	1	4	yes	—
371	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
372	C₄	C₂×C₁₉×#120	1	2	yes	—
373	C₂	—	2	4	no	—
374	C₂	—	2	8	no	—
375	C₂	—	4	16	no	—
376	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
377	C₂	C₂×C₁₉×#418	1	2	yes	—
378	C₂	C₁₉×#3003	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×D₄×C₁₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₉×#418	C₂	semidirect
3. C₂×C₁₉×#407	C₂	semidirect
4. C₁₉×#2280	C₂	semidirect
5. C₁₉×#1786	C₂	semidirect
11. C₂³×D₄×C₁₉	C₄	semidirect
15. C₂²×M₁₆×C₁₉	C₂²	semidirect
16. C₂×C₁₉×#117	C₂²	semidirect
18. C₂×C₁₉×#102	C₂²	semidirect
20. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
22. C₁₉×#380	C₂²	semidirect
56. C₂²×C₈×C₁₉	C₂³	semidirect
58. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
93. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
119. #20598	C₁₉	direct (N × H)
164. C₂×#418	C₂×C₁₉	semidirect
165. C₂×#407	C₂×C₁₉	semidirect
166. #2280	C₂×C₁₉	semidirect
167. #1786	C₂×C₁₉	semidirect
180. C₂²×C₁₉	#418	semidirect
194. C₂³×D₄	C₄×C₁₉	semidirect
198. C₂²×M₁₆	C₂²×C₁₉	semidirect
199. C₂×#117	C₂²×C₁₉	semidirect
201. C₂×#102	C₂²×C₁₉	semidirect
203. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
205. #380	C₂²×C₁₉	semidirect
245. C₂²×C₈	C₂³×C₁₉	semidirect
247. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
254. C₁₉	#20598	direct (N × H)
283. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
364. C₂²	C₁₉×#418	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×D₄×C₁₉	2
C₂×C₁₉×#418	2
C₂×C₁₉×#407	2
C₁₉×#2280	2
C₁₉×#1786	2
#20598	19

Subgroups — C19×#20598 #18026557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20598 #18026557